estimates for semi-degenerate simplex multipliers
Robert Kesler
Santa Monica, USA
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Abstract
Muscalu, Tao, and Thiele prove estimates for the "Biest" operator defined on Schwartz functions by the map
via a time-frequency argument that produces bounds for all multipliers with non-degenerate trilinear simplex symbols. In this article we prove estimates for a pair of simplex multipliers defined on Schwartz functions by the maps
for which the non-degeneracy condition fails. Our argument combines the standard -based energy with an -based energy in order to enable summability over various size parameters. As a consequence, we obtain that maps into for all and maps into for all . Both target ranges are shown to be sharp.
Cite this article
Robert Kesler, estimates for semi-degenerate simplex multipliers. Rev. Mat. Iberoam. 36 (2020), no. 1, pp. 99–158
DOI 10.4171/RMI/1123